/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 \(3 x+7-2 x=0\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 65

\(3 x+7-2 x=0\)

Short Answer

Expert verified
x = -7

Step by step solution

01

Combine Like Terms

Combine the terms involving x: \(3x - 2x + 7 = 0\). This simplifies to \(x + 7 = 0\).
02

Isolate the Variable

Subtract 7 from both sides to isolate the variable x: \(x + 7 - 7 = -7\). This simplifies to \(x = -7\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

combine like terms
When solving linear equations like the exercise example of \(3x + 7 - 2x = 0\), one of the first steps you will often have to do is to combine like terms.
Like terms are terms that have the exact same variable part. For instance, in our example, \(3x\) and \(2x\) are like terms because both terms contain the variable \(x\). The process involves combining these similar terms to simplify the equation.
In the example, combining \(3x\) and \(2x\) like terms, we get:
\[3x - 2x = x.\]
Hence, the equation simplifies to \(x + 7 = 0\). Being able to combine like terms quickly makes working with equations much easier.
isolate the variable
The next crucial step in solving linear equations is to isolate the variable. This means making the variable stand alone on one side of the equation so that we can find out its value.
With our simplified equation \(x + 7 = 0\), we need to get \(x\) by itself.
We've added 7 to \(x\), so the opposite operation we will use is subtraction.
Subtract 7 from both sides:
\[x + 7 - 7 = 0 - 7\]
This further simplifies to:
\[x = -7\]
Now, the variable \(x\) is isolated, and we can see that \(x = -7\).
simplify equations
Simplifying equations helps to clear the path to solving for the variable by making the equation as straightforward as possible.
When you combine like terms and isolate the variable, you are in essence simplifying the equation.
The purpose of simplification is to make it easier to handle the equation and to clearly see the steps you need to take.
Starting from \(3x + 7 - 2x = 0\), through combining like terms, you simplified it to \(x + 7 = 0\). Simplifying further by isolating the variable, you reached \(x = -7\).
Each step along the way made the equation simpler to handle.
This clear and simplified pathway is a fundamental strategy in solving linear equations effectively.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In one day, a store sold \(\frac{2}{3}\) as many DVDs as Blu-ray discs. The total number of DVDs and Blu-ray discs sold that day was \(280 .\) How many DVDs were sold?

During the 115 th session, the total number of Democrats and Republicans in the U.S. House of Representatives was \(434 .\) There were 46 more Republicans than Democrats. How many members of each party were there? (Data from www.house.gov)

The sum of the measures of the angles of any triangle is \(180^{\circ} .\) In triangle \(A B C\), angles \(A\) and \(B\) have the same measure, while the measure of angle \(C\) is \(60^{\circ}\) greater than each of angles \(A\) and \(B\). What are the measures of the three angles?

Solve each formula for the specified variable. \(A=p(1+r t)\) for \(t\)

Find the measure of an angle such that the sum of the measures of its complement and its supplement is \(160^{\circ} .\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.